In this paper, a method is presented for the solution of general frictionless nonlinear contact-impact problems called "United Elements". In the fields of mechanics and structures, contact-impact problems are considered one of the most difficult fields. The reason is that in addition to the presence of material and geometric nonlinearities, the last possible nonlinearity, the boundary condition nonlinearity, enters the problem. In fact, the boundary condition will be obtained as a part of the solution. The usual methods for these problems stem from Lagrange Multipliers and Penalty Function methods, and in each method, the simultaneous satisfaction of contact constraints and equilibrium equations is sought. Both of these methods have some intrinsic mathematical and numerical deficiencies which relates to the quality of boundary condition exertion. Therefore, in this work, bayed on the physical concepts and mechanics principals, another method is used for the solution of contact-impact problems. The method is" not only suitable for computer programming but also compensates the deficiencies of the other methods.